Does Gödel Matter? by Jordan Ellenberg (reviewing Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein)
The reticent and relentlessly abstract logician Kurt Gödel might seem an unlikely candidate for popular appreciation. But that's what Rebecca Goldstein aims for in her new book Incompleteness, an account of Gödel's most famous theorem, which was announced 75 years ago this October. Goldstein calls Gödel's incompleteness theorem "the third leg, together with Heisenberg's uncertainty principle and Einstein's relativity, of that tripod of theoretical cataclysms that have been felt to force disturbances deep down in the foundations of the 'exact sciences.' "
The Original Computer Geek by Clive Thomson (reviewing Dark Hero Of The Information Age: In Search of Norbert Wiener The Father of Cybernetics by Flo Conway and Jim Siegelman)
Posted by John at March 21, 2005 11:40 AMTo be a truly famous scientist, you need to have a hit single. Einstein had E = mc2. Newton had the apple and gravity. Even the lesser rock-star scientists have one shining achievement for which they're known -- such as Niels Bohr's theory of the atom.
But there's another kind of scientist who never breaks through, usually because while his discovery is revolutionary it's also maddeningly hard to summarize in a simple sentence or two. He never produces a catchy hit single. He's more like a back-room influencer: his work inspires dozens of other innovators who absorb the idea, produce more easily comprehensible innovations and become more famous than their mentor could have dreamed. Find an influencer, and you'll find a deeply bitter man.
Norbert Wiener -- the inventor of ''cybernetics'' -- is precisely this type of scientist. Odds are that you are only dimly aware of cybernetics, if at all. (A friend asked me, ''Isn't that like Dianetics?'') ''Dark Hero of the Information Age,'' by the journalists Flo Conway and Jim Siegelman, intends to correct this, but their book struggles with the circular tautologies of fame: it must continually plead the case of why the guy ought to have been better known.
I wonder why Goedel's incompleteness theorem seems so significant to people. I used to be fascinated by it myself (although, to be honest, it still puzzles me sometimes that no TM can prove the (objective) truths about all TMs (i.e. whether they halt), although humans can seemingly do it. Am I starting to sound like Penrose? I hope not, since I "believe" that humans' computational powers are no different than computers).
My guess is that people have a straw man of the formalist program, i.e. they think that some people would believe that all mathematical truths can be decided by one axiomatic system. And when this is shown to be impossible, they consider logicism and all similar ideas to be doomed. Maybe it's a case of "associative thinking".
Posted by: Gustavo Lacerda at March 22, 2005 07:38 PM